ocaml: phase 5.1 dp_word_break.ml baseline (4/5 strings segmentable)

Classic word-break DP — for each position i, check whether any
dictionary word ends at i with a prior reachable position:

  dp[i] = exists w in dict with wl <= i and
          dp[i - wl] && s.sub (i - wl) wl = w

Dictionary: apple, pen, pine, pineapple, cats, cat, and, sand, dog
Inputs:
  applepenapple        yes  (apple pen apple)
  pineapplepenapple    yes  (pineapple pen apple)
  catsanddog           yes  (cats and dog)
  catsandog            no   (no segmentation reaches the end)
  applesand            yes  (apple sand)

Tests bool-typed Array, String.sub primitive, nested List.iter
over the dict inside for-loop over end positions, closure capture
of the outer dp.

179 baseline programs total.

plans/ocaml-on-sx.md

@@ -407,6 +407,14 @@ _Newest first._
   binary search tree (`type 'a tree = Leaf | Node of 'a * 'a tree *
   'a tree`) with insert + in-order traversal. Tests parametric ADT,
   recursive match, List.append, List.fold_left.
+- 2026-05-11 Phase 5.1 — dp_word_break.ml baseline (word-break DP
+  over 5 strings with 9-word dictionary; 4 strings segmentable).
+  dp[i] = ∃ word w of length wl ≤ i with prefix s[i−wl..i]=w and
+  dp[i−wl]=true. Inputs: applepenapple, pineapplepenapple,
+  catsanddog (yes); catsandog (no — leftover "og"); applesand (yes).
+  Tests bool-typed DP array, `String.sub s start len` substring
+  primitive, nested List.iter over dict inside for-loop over
+  positions, short-circuit + closure. 179 baseline programs total.
 - 2026-05-11 Phase 5.1 — histogram_area.ml baseline (largest
   rectangle in histogram [2;1;5;6;2;3] = 10). Linear-time stack
   algorithm: push indices while heights are non-decreasing; on